I'm having a little trouble connecting the dots between what you put at the top and your question.
What I see is :
(1) Definition of Forms for Plato / God's Ideas for Augustine as immutable and eternal entities.
(2) If always 1 + 1 = 2, then 1+ 1. Ergo, this is eternal and immutable.
What I'm missing is the precise question you are asking as it relates to (1) and (2). As worded, I would say that (2) holds (being merely definitional -- something that is always is true eternally and immutably true) but does not necessarily force upon us the conclusion (1).
Specifically, I see two moves hidden between (2) and (1) that undermine the necessity. First, (1) posits eternal, immutable entities about substantive things in the world (Plato believes there's a form of horse, for instance) whereas (2) posits only a invariant proportion as eternal and immutable (which has no perfect physical instantiation).
Second, the argument in (2) is in Kant's vocabulary a priori and "synthetic" -- meaning that the manipulation is wholly contained in the definitions that 1 + 1 = 2 (synthesis of two incidents of the concept 1). Thus, it's not entirely clear that we are saying anything eternal or immutable so much as we are rearranging words. And that we can make this statement using only the reason we have (a priori).
Conversely, substantive forms/ideas are substantiated by objects in the world (either through the activity of the demiurge or the creator) as reflections on it. None of that is necessary to accept the continued veracity of 1 + 1 = 2.
To accept (2) is roughly to be committed to Mathematical Platonism.
Separately, not everyone is committed to the eternal truth of 1 + 1 = 2. There are also other positions that posit that this is a function of our mental apparatus rather than reality. (See for instance the considerations at http://www.math.harvard.edu/~mazur/papers/plato4.pdf ).
More generally, if your question is what other ways do people manage this than "ideas", then the answers that come to mind specifically (moving through history) are roughly in two categories:
Aristotle's essentialism. Aristotle thinks we get the real essences by abstracting essences from the objects we encounter. (differs mainly in that for Plato we recollect forms through anamnesis / for Augustine, we are helped by divine illumination ).
Conceptualisms - views where we have "concepts" in our mind but that these don't exist out there in things. One medieval version is called "Nominalism." This is generally the dominant view type today.
Kant's categories - sum of categories in the mind and features we encounter subsumed under these. (Hegel also has a type of category theory -- at least at points).
I could say more ... but I'm not sure which part is closest to the question you are asking.